Problem: Rewrite as a simplified fraction. ${2.8\overline{13} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2813.1313...\\ 10x &= 28.1313...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2785}$ ${x = \dfrac{2785}{990}} $ ${x = \dfrac{557}{198}} \text{or} {2 \dfrac{161}{198}}$